TSTP Solution File: ALG081+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG081+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:02:15 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 69
% Syntax : Number of clauses : 220 ( 212 unt; 8 nHn; 220 RR)
% Number of literals : 240 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(e12,e10),
file('ALG081+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e14,e10),
file('ALG081+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e14,e12),
file('ALG081+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e21,e20),
file('ALG081+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(e23,e20),
file('ALG081+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(e24,e20),
file('ALG081+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(e24,e21),
file('ALG081+1.p',unknown),
[] ).
cnf(19,axiom,
~ equal(e24,e22),
file('ALG081+1.p',unknown),
[] ).
cnf(46,axiom,
equal(h(j(e20)),e20),
file('ALG081+1.p',unknown),
[] ).
cnf(47,axiom,
equal(h(j(e21)),e21),
file('ALG081+1.p',unknown),
[] ).
cnf(50,axiom,
equal(h(j(e24)),e24),
file('ALG081+1.p',unknown),
[] ).
cnf(51,axiom,
equal(j(h(e10)),e10),
file('ALG081+1.p',unknown),
[] ).
cnf(52,axiom,
equal(j(h(e11)),e11),
file('ALG081+1.p',unknown),
[] ).
cnf(53,axiom,
equal(j(h(e12)),e12),
file('ALG081+1.p',unknown),
[] ).
cnf(54,axiom,
equal(j(h(e13)),e13),
file('ALG081+1.p',unknown),
[] ).
cnf(55,axiom,
equal(j(h(e14)),e14),
file('ALG081+1.p',unknown),
[] ).
cnf(56,axiom,
equal(op1(e10,e10),e10),
file('ALG081+1.p',unknown),
[] ).
cnf(59,axiom,
equal(op1(e10,e13),e13),
file('ALG081+1.p',unknown),
[] ).
cnf(62,axiom,
equal(op1(e11,e11),e12),
file('ALG081+1.p',unknown),
[] ).
cnf(63,axiom,
equal(op1(e11,e12),e13),
file('ALG081+1.p',unknown),
[] ).
cnf(64,axiom,
equal(op1(e11,e13),e14),
file('ALG081+1.p',unknown),
[] ).
cnf(66,axiom,
equal(op1(e12,e10),e12),
file('ALG081+1.p',unknown),
[] ).
cnf(68,axiom,
equal(op1(e12,e12),e11),
file('ALG081+1.p',unknown),
[] ).
cnf(69,axiom,
equal(op1(e12,e13),e10),
file('ALG081+1.p',unknown),
[] ).
cnf(71,axiom,
equal(op1(e13,e10),e13),
file('ALG081+1.p',unknown),
[] ).
cnf(72,axiom,
equal(op1(e13,e11),e10),
file('ALG081+1.p',unknown),
[] ).
cnf(76,axiom,
equal(op1(e14,e10),e14),
file('ALG081+1.p',unknown),
[] ).
cnf(78,axiom,
equal(op1(e14,e12),e10),
file('ALG081+1.p',unknown),
[] ).
cnf(87,axiom,
equal(op2(e21,e21),e22),
file('ALG081+1.p',unknown),
[] ).
cnf(88,axiom,
equal(op2(e21,e22),e24),
file('ALG081+1.p',unknown),
[] ).
cnf(89,axiom,
equal(op2(e21,e23),e20),
file('ALG081+1.p',unknown),
[] ).
cnf(90,axiom,
equal(op2(e21,e24),e23),
file('ALG081+1.p',unknown),
[] ).
cnf(91,axiom,
equal(op2(e22,e20),e22),
file('ALG081+1.p',unknown),
[] ).
cnf(93,axiom,
equal(op2(e22,e22),e23),
file('ALG081+1.p',unknown),
[] ).
cnf(94,axiom,
equal(op2(e22,e23),e24),
file('ALG081+1.p',unknown),
[] ).
cnf(95,axiom,
equal(op2(e22,e24),e21),
file('ALG081+1.p',unknown),
[] ).
cnf(96,axiom,
equal(op2(e23,e20),e23),
file('ALG081+1.p',unknown),
[] ).
cnf(97,axiom,
equal(op2(e23,e21),e24),
file('ALG081+1.p',unknown),
[] ).
cnf(99,axiom,
equal(op2(e23,e23),e21),
file('ALG081+1.p',unknown),
[] ).
cnf(100,axiom,
equal(op2(e23,e24),e22),
file('ALG081+1.p',unknown),
[] ).
cnf(101,axiom,
equal(op2(e24,e20),e24),
file('ALG081+1.p',unknown),
[] ).
cnf(103,axiom,
equal(op2(e24,e22),e21),
file('ALG081+1.p',unknown),
[] ).
cnf(104,axiom,
equal(op2(e24,e23),e22),
file('ALG081+1.p',unknown),
[] ).
cnf(105,axiom,
equal(op2(e24,e24),e20),
file('ALG081+1.p',unknown),
[] ).
cnf(109,axiom,
equal(op2(h(e10),h(e13)),h(op1(e10,e13))),
file('ALG081+1.p',unknown),
[] ).
cnf(112,axiom,
equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
file('ALG081+1.p',unknown),
[] ).
cnf(113,axiom,
equal(op2(h(e11),h(e12)),h(op1(e11,e12))),
file('ALG081+1.p',unknown),
[] ).
cnf(116,axiom,
equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
file('ALG081+1.p',unknown),
[] ).
cnf(119,axiom,
equal(op2(h(e12),h(e13)),h(op1(e12,e13))),
file('ALG081+1.p',unknown),
[] ).
cnf(121,axiom,
equal(op2(h(e13),h(e10)),h(op1(e13,e10))),
file('ALG081+1.p',unknown),
[] ).
cnf(122,axiom,
equal(op2(h(e13),h(e11)),h(op1(e13,e11))),
file('ALG081+1.p',unknown),
[] ).
cnf(126,axiom,
equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
file('ALG081+1.p',unknown),
[] ).
cnf(128,axiom,
equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
file('ALG081+1.p',unknown),
[] ).
cnf(137,axiom,
equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
file('ALG081+1.p',unknown),
[] ).
cnf(138,axiom,
equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
file('ALG081+1.p',unknown),
[] ).
cnf(139,axiom,
equal(op1(j(e21),j(e23)),j(op2(e21,e23))),
file('ALG081+1.p',unknown),
[] ).
cnf(140,axiom,
equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
file('ALG081+1.p',unknown),
[] ).
cnf(141,axiom,
equal(op1(j(e22),j(e20)),j(op2(e22,e20))),
file('ALG081+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
file('ALG081+1.p',unknown),
[] ).
cnf(144,axiom,
equal(op1(j(e22),j(e23)),j(op2(e22,e23))),
file('ALG081+1.p',unknown),
[] ).
cnf(145,axiom,
equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
file('ALG081+1.p',unknown),
[] ).
cnf(146,axiom,
equal(op1(j(e23),j(e20)),j(op2(e23,e20))),
file('ALG081+1.p',unknown),
[] ).
cnf(149,axiom,
equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
file('ALG081+1.p',unknown),
[] ).
cnf(150,axiom,
equal(op1(j(e23),j(e24)),j(op2(e23,e24))),
file('ALG081+1.p',unknown),
[] ).
cnf(153,axiom,
equal(op1(j(e24),j(e22)),j(op2(e24,e22))),
file('ALG081+1.p',unknown),
[] ).
cnf(154,axiom,
equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
file('ALG081+1.p',unknown),
[] ).
cnf(155,axiom,
equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
file('ALG081+1.p',unknown),
[] ).
cnf(164,axiom,
( equal(h(e11),e24)
| equal(h(e11),e23)
| equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
file('ALG081+1.p',unknown),
[] ).
cnf(165,axiom,
( equal(h(e10),e24)
| equal(h(e10),e23)
| equal(h(e10),e22)
| equal(h(e10),e21)
| equal(h(e10),e20) ),
file('ALG081+1.p',unknown),
[] ).
cnf(166,plain,
equal(op1(j(e24),j(e24)),j(e20)),
inference(rew,[status(thm),theory(equality)],[105,155]),
[iquote('0:Rew:105.0,155.0')] ).
cnf(167,plain,
equal(op1(j(e24),j(e23)),j(e22)),
inference(rew,[status(thm),theory(equality)],[104,154]),
[iquote('0:Rew:104.0,154.0')] ).
cnf(168,plain,
equal(op1(j(e24),j(e22)),j(e21)),
inference(rew,[status(thm),theory(equality)],[103,153]),
[iquote('0:Rew:103.0,153.0')] ).
cnf(171,plain,
equal(op1(j(e23),j(e24)),j(e22)),
inference(rew,[status(thm),theory(equality)],[100,150]),
[iquote('0:Rew:100.0,150.0')] ).
cnf(172,plain,
equal(op1(j(e23),j(e23)),j(e21)),
inference(rew,[status(thm),theory(equality)],[99,149]),
[iquote('0:Rew:99.0,149.0')] ).
cnf(175,plain,
equal(op1(j(e23),j(e20)),j(e23)),
inference(rew,[status(thm),theory(equality)],[96,146]),
[iquote('0:Rew:96.0,146.0')] ).
cnf(176,plain,
equal(op1(j(e22),j(e24)),j(e21)),
inference(rew,[status(thm),theory(equality)],[95,145]),
[iquote('0:Rew:95.0,145.0')] ).
cnf(177,plain,
equal(op1(j(e22),j(e23)),j(e24)),
inference(rew,[status(thm),theory(equality)],[94,144]),
[iquote('0:Rew:94.0,144.0')] ).
cnf(178,plain,
equal(op1(j(e22),j(e22)),j(e23)),
inference(rew,[status(thm),theory(equality)],[93,143]),
[iquote('0:Rew:93.0,143.0')] ).
cnf(180,plain,
equal(op1(j(e22),j(e20)),j(e22)),
inference(rew,[status(thm),theory(equality)],[91,141]),
[iquote('0:Rew:91.0,141.0')] ).
cnf(181,plain,
equal(op1(j(e21),j(e24)),j(e23)),
inference(rew,[status(thm),theory(equality)],[90,140]),
[iquote('0:Rew:90.0,140.0')] ).
cnf(182,plain,
equal(op1(j(e21),j(e23)),j(e20)),
inference(rew,[status(thm),theory(equality)],[89,139]),
[iquote('0:Rew:89.0,139.0')] ).
cnf(183,plain,
equal(op1(j(e21),j(e22)),j(e24)),
inference(rew,[status(thm),theory(equality)],[88,138]),
[iquote('0:Rew:88.0,138.0')] ).
cnf(184,plain,
equal(op1(j(e21),j(e21)),j(e22)),
inference(rew,[status(thm),theory(equality)],[87,137]),
[iquote('0:Rew:87.0,137.0')] ).
cnf(193,plain,
equal(op2(h(e14),h(e12)),h(e10)),
inference(rew,[status(thm),theory(equality)],[78,128]),
[iquote('0:Rew:78.0,128.0')] ).
cnf(195,plain,
equal(op2(h(e14),h(e10)),h(e14)),
inference(rew,[status(thm),theory(equality)],[76,126]),
[iquote('0:Rew:76.0,126.0')] ).
cnf(199,plain,
equal(op2(h(e13),h(e11)),h(e10)),
inference(rew,[status(thm),theory(equality)],[72,122]),
[iquote('0:Rew:72.0,122.0')] ).
cnf(200,plain,
equal(op2(h(e13),h(e10)),h(e13)),
inference(rew,[status(thm),theory(equality)],[71,121]),
[iquote('0:Rew:71.0,121.0')] ).
cnf(202,plain,
equal(op2(h(e12),h(e13)),h(e10)),
inference(rew,[status(thm),theory(equality)],[69,119]),
[iquote('0:Rew:69.0,119.0')] ).
cnf(205,plain,
equal(op2(h(e12),h(e10)),h(e12)),
inference(rew,[status(thm),theory(equality)],[66,116]),
[iquote('0:Rew:66.0,116.0')] ).
cnf(208,plain,
equal(op2(h(e11),h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[63,113]),
[iquote('0:Rew:63.0,113.0')] ).
cnf(209,plain,
equal(op2(h(e11),h(e11)),h(e12)),
inference(rew,[status(thm),theory(equality)],[62,112]),
[iquote('0:Rew:62.0,112.0')] ).
cnf(212,plain,
equal(op2(h(e10),h(e13)),h(e13)),
inference(rew,[status(thm),theory(equality)],[59,109]),
[iquote('0:Rew:59.0,109.0')] ).
cnf(216,plain,
equal(h(e10),e24),
inference(spt,[spt(split,[position(s1)])],[165]),
[iquote('1:Spt:165.0')] ).
cnf(217,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[216,51]),
[iquote('1:Rew:216.0,51.0')] ).
cnf(232,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[217,166]),
[iquote('1:Rew:217.0,166.0')] ).
cnf(237,plain,
equal(op1(j(e23),e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[217,171]),
[iquote('1:Rew:217.0,171.0')] ).
cnf(239,plain,
equal(op1(j(e22),e10),j(e21)),
inference(rew,[status(thm),theory(equality)],[217,176]),
[iquote('1:Rew:217.0,176.0')] ).
cnf(246,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,232]),
[iquote('1:Rew:56.0,232.0')] ).
cnf(249,plain,
equal(op1(j(e23),e10),j(e23)),
inference(rew,[status(thm),theory(equality)],[246,175]),
[iquote('1:Rew:246.0,175.0')] ).
cnf(251,plain,
equal(op1(j(e22),e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[246,180]),
[iquote('1:Rew:246.0,180.0')] ).
cnf(252,plain,
equal(op1(j(e21),j(e23)),e10),
inference(rew,[status(thm),theory(equality)],[246,182]),
[iquote('1:Rew:246.0,182.0')] ).
cnf(262,plain,
equal(j(e23),j(e22)),
inference(rew,[status(thm),theory(equality)],[237,249]),
[iquote('1:Rew:237.0,249.0')] ).
cnf(264,plain,
equal(op1(j(e22),j(e22)),j(e21)),
inference(rew,[status(thm),theory(equality)],[262,172]),
[iquote('1:Rew:262.0,172.0')] ).
cnf(276,plain,
equal(j(e22),j(e21)),
inference(rew,[status(thm),theory(equality)],[239,251]),
[iquote('1:Rew:239.0,251.0')] ).
cnf(283,plain,
equal(j(e23),j(e21)),
inference(rew,[status(thm),theory(equality)],[276,262]),
[iquote('1:Rew:276.0,262.0')] ).
cnf(287,plain,
equal(op1(j(e21),j(e21)),e10),
inference(rew,[status(thm),theory(equality)],[283,252]),
[iquote('1:Rew:283.0,252.0')] ).
cnf(297,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[287,264,276]),
[iquote('1:Rew:287.0,264.0,276.0,264.0')] ).
cnf(298,plain,
equal(h(e10),e21),
inference(rew,[status(thm),theory(equality)],[297,47]),
[iquote('1:Rew:297.0,47.0')] ).
cnf(304,plain,
equal(e24,e21),
inference(rew,[status(thm),theory(equality)],[216,298]),
[iquote('1:Rew:216.0,298.0')] ).
cnf(305,plain,
$false,
inference(mrr,[status(thm)],[304,17]),
[iquote('1:MRR:304.0,17.0')] ).
cnf(308,plain,
~ equal(h(e10),e24),
inference(spt,[spt(split,[position(sa)])],[305,216]),
[iquote('1:Spt:305.0,165.0,216.0')] ).
cnf(309,plain,
( equal(h(e10),e23)
| equal(h(e10),e22)
| equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2)])],[165]),
[iquote('1:Spt:305.0,165.1,165.2,165.3,165.4')] ).
cnf(310,plain,
equal(h(e10),e23),
inference(spt,[spt(split,[position(s2s1)])],[309]),
[iquote('2:Spt:309.0')] ).
cnf(311,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[310,51]),
[iquote('2:Rew:310.0,51.0')] ).
cnf(328,plain,
equal(op1(j(e22),e10),j(e24)),
inference(rew,[status(thm),theory(equality)],[311,177]),
[iquote('2:Rew:311.0,177.0')] ).
cnf(338,plain,
equal(op1(e10,e10),j(e21)),
inference(rew,[status(thm),theory(equality)],[311,172]),
[iquote('2:Rew:311.0,172.0')] ).
cnf(341,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[56,338]),
[iquote('2:Rew:56.0,338.0')] ).
cnf(349,plain,
equal(op1(e10,e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[341,184]),
[iquote('2:Rew:341.0,184.0')] ).
cnf(352,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[56,349]),
[iquote('2:Rew:56.0,349.0')] ).
cnf(359,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[56,328,352]),
[iquote('2:Rew:56.0,328.0,352.0,328.0')] ).
cnf(363,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[359,166]),
[iquote('2:Rew:359.0,166.0')] ).
cnf(367,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,363]),
[iquote('2:Rew:56.0,363.0')] ).
cnf(368,plain,
equal(h(e10),e20),
inference(rew,[status(thm),theory(equality)],[367,46]),
[iquote('2:Rew:367.0,46.0')] ).
cnf(372,plain,
equal(e23,e20),
inference(rew,[status(thm),theory(equality)],[310,368]),
[iquote('2:Rew:310.0,368.0')] ).
cnf(373,plain,
$false,
inference(mrr,[status(thm)],[372,13]),
[iquote('2:MRR:372.0,13.0')] ).
cnf(385,plain,
~ equal(h(e10),e23),
inference(spt,[spt(split,[position(s2sa)])],[373,310]),
[iquote('2:Spt:373.0,309.0,310.0')] ).
cnf(386,plain,
( equal(h(e10),e22)
| equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2)])],[309]),
[iquote('2:Spt:373.0,309.1,309.2,309.3')] ).
cnf(387,plain,
equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2s1)])],[386]),
[iquote('3:Spt:386.0')] ).
cnf(389,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[387,51]),
[iquote('3:Rew:387.0,51.0')] ).
cnf(405,plain,
equal(op1(e10,e10),j(e23)),
inference(rew,[status(thm),theory(equality)],[389,178]),
[iquote('3:Rew:389.0,178.0')] ).
cnf(409,plain,
equal(op1(e10,j(e23)),j(e24)),
inference(rew,[status(thm),theory(equality)],[389,177]),
[iquote('3:Rew:389.0,177.0')] ).
cnf(419,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[56,405]),
[iquote('3:Rew:56.0,405.0')] ).
cnf(448,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[56,409,419]),
[iquote('3:Rew:56.0,409.0,419.0,409.0')] ).
cnf(449,plain,
equal(h(e10),e24),
inference(rew,[status(thm),theory(equality)],[448,50]),
[iquote('3:Rew:448.0,50.0')] ).
cnf(452,plain,
equal(e24,e22),
inference(rew,[status(thm),theory(equality)],[387,449]),
[iquote('3:Rew:387.0,449.0')] ).
cnf(453,plain,
$false,
inference(mrr,[status(thm)],[452,19]),
[iquote('3:MRR:452.0,19.0')] ).
cnf(466,plain,
~ equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2sa)])],[453,387]),
[iquote('3:Spt:453.0,386.0,387.0')] ).
cnf(467,plain,
( equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2s2)])],[386]),
[iquote('3:Spt:453.0,386.1,386.2')] ).
cnf(468,plain,
equal(h(e10),e21),
inference(spt,[spt(split,[position(s2s2s2s1)])],[467]),
[iquote('4:Spt:467.0')] ).
cnf(470,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[468,51]),
[iquote('4:Rew:468.0,51.0')] ).
cnf(487,plain,
equal(op1(e10,j(e22)),j(e24)),
inference(rew,[status(thm),theory(equality)],[470,183]),
[iquote('4:Rew:470.0,183.0')] ).
cnf(491,plain,
equal(op1(e10,e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[470,184]),
[iquote('4:Rew:470.0,184.0')] ).
cnf(501,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[56,491]),
[iquote('4:Rew:56.0,491.0')] ).
cnf(518,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[56,487,501]),
[iquote('4:Rew:56.0,487.0,501.0,487.0')] ).
cnf(522,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[518,166]),
[iquote('4:Rew:518.0,166.0')] ).
cnf(525,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,522]),
[iquote('4:Rew:56.0,522.0')] ).
cnf(526,plain,
equal(h(e10),e20),
inference(rew,[status(thm),theory(equality)],[525,46]),
[iquote('4:Rew:525.0,46.0')] ).
cnf(530,plain,
equal(e21,e20),
inference(rew,[status(thm),theory(equality)],[468,526]),
[iquote('4:Rew:468.0,526.0')] ).
cnf(531,plain,
$false,
inference(mrr,[status(thm)],[530,11]),
[iquote('4:MRR:530.0,11.0')] ).
cnf(544,plain,
~ equal(h(e10),e21),
inference(spt,[spt(split,[position(s2s2s2sa)])],[531,468]),
[iquote('4:Spt:531.0,467.0,468.0')] ).
cnf(545,plain,
equal(h(e10),e20),
inference(spt,[spt(split,[position(s2s2s2s2)])],[467]),
[iquote('4:Spt:531.0,467.1')] ).
cnf(548,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[545,51]),
[iquote('4:Rew:545.0,51.0')] ).
cnf(552,plain,
equal(op2(h(e14),h(e12)),e20),
inference(rew,[status(thm),theory(equality)],[545,193]),
[iquote('4:Rew:545.0,193.0')] ).
cnf(553,plain,
equal(op2(h(e14),e20),h(e14)),
inference(rew,[status(thm),theory(equality)],[545,195]),
[iquote('4:Rew:545.0,195.0')] ).
cnf(554,plain,
equal(op2(h(e13),h(e11)),e20),
inference(rew,[status(thm),theory(equality)],[545,199]),
[iquote('4:Rew:545.0,199.0')] ).
cnf(555,plain,
equal(op2(h(e13),e20),h(e13)),
inference(rew,[status(thm),theory(equality)],[545,200]),
[iquote('4:Rew:545.0,200.0')] ).
cnf(556,plain,
equal(op2(h(e12),h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[545,202]),
[iquote('4:Rew:545.0,202.0')] ).
cnf(557,plain,
equal(op2(h(e12),e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[545,205]),
[iquote('4:Rew:545.0,205.0')] ).
cnf(561,plain,
equal(op2(e20,h(e13)),h(e13)),
inference(rew,[status(thm),theory(equality)],[545,212]),
[iquote('4:Rew:545.0,212.0')] ).
cnf(579,plain,
equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
[iquote('5:Spt:164.0')] ).
cnf(587,plain,
equal(op2(e24,h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[579,208]),
[iquote('5:Rew:579.0,208.0')] ).
cnf(588,plain,
equal(op2(e24,e24),h(e12)),
inference(rew,[status(thm),theory(equality)],[579,209]),
[iquote('5:Rew:579.0,209.0')] ).
cnf(608,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[105,588]),
[iquote('5:Rew:105.0,588.0')] ).
cnf(615,plain,
equal(op2(e20,h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[608,556]),
[iquote('5:Rew:608.0,556.0')] ).
cnf(629,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[561,615]),
[iquote('5:Rew:561.0,615.0')] ).
cnf(650,plain,
equal(e24,e20),
inference(rew,[status(thm),theory(equality)],[101,587,608,629]),
[iquote('5:Rew:101.0,587.0,608.0,587.0,629.0,587.0')] ).
cnf(651,plain,
$false,
inference(mrr,[status(thm)],[650,14]),
[iquote('5:MRR:650.0,14.0')] ).
cnf(656,plain,
~ equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2sa)])],[651,579]),
[iquote('5:Spt:651.0,164.0,579.0')] ).
cnf(657,plain,
( equal(h(e11),e23)
| equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2)])],[164]),
[iquote('5:Spt:651.0,164.1,164.2,164.3,164.4')] ).
cnf(658,plain,
equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[657]),
[iquote('6:Spt:657.0')] ).
cnf(665,plain,
equal(op2(e23,e23),h(e12)),
inference(rew,[status(thm),theory(equality)],[658,209]),
[iquote('6:Rew:658.0,209.0')] ).
cnf(666,plain,
equal(op2(e23,h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[658,208]),
[iquote('6:Rew:658.0,208.0')] ).
cnf(686,plain,
equal(h(e12),e21),
inference(rew,[status(thm),theory(equality)],[99,665]),
[iquote('6:Rew:99.0,665.0')] ).
cnf(687,plain,
equal(j(e21),e12),
inference(rew,[status(thm),theory(equality)],[686,53]),
[iquote('6:Rew:686.0,53.0')] ).
cnf(699,plain,
equal(op1(e12,e12),j(e22)),
inference(rew,[status(thm),theory(equality)],[687,184]),
[iquote('6:Rew:687.0,184.0')] ).
cnf(703,plain,
equal(op1(j(e24),j(e22)),e12),
inference(rew,[status(thm),theory(equality)],[687,168]),
[iquote('6:Rew:687.0,168.0')] ).
cnf(707,plain,
equal(j(e22),e11),
inference(rew,[status(thm),theory(equality)],[68,699]),
[iquote('6:Rew:68.0,699.0')] ).
cnf(718,plain,
equal(h(e13),e24),
inference(rew,[status(thm),theory(equality)],[97,666,686]),
[iquote('6:Rew:97.0,666.0,686.0,666.0')] ).
cnf(719,plain,
equal(j(e24),e13),
inference(rew,[status(thm),theory(equality)],[718,54]),
[iquote('6:Rew:718.0,54.0')] ).
cnf(772,plain,
equal(e12,e10),
inference(rew,[status(thm),theory(equality)],[72,703,719,707]),
[iquote('6:Rew:72.0,703.0,719.0,703.0,707.0,703.0')] ).
cnf(773,plain,
$false,
inference(mrr,[status(thm)],[772,2]),
[iquote('6:MRR:772.0,2.0')] ).
cnf(774,plain,
~ equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[773,658]),
[iquote('6:Spt:773.0,657.0,658.0')] ).
cnf(775,plain,
( equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[657]),
[iquote('6:Spt:773.0,657.1,657.2,657.3')] ).
cnf(776,plain,
equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[775]),
[iquote('7:Spt:775.0')] ).
cnf(778,plain,
equal(j(e22),e11),
inference(rew,[status(thm),theory(equality)],[776,52]),
[iquote('7:Rew:776.0,52.0')] ).
cnf(791,plain,
equal(op2(e22,e22),h(e12)),
inference(rew,[status(thm),theory(equality)],[776,209]),
[iquote('7:Rew:776.0,209.0')] ).
cnf(799,plain,
equal(op1(e11,j(e23)),j(e24)),
inference(rew,[status(thm),theory(equality)],[778,177]),
[iquote('7:Rew:778.0,177.0')] ).
cnf(805,plain,
equal(h(e12),e23),
inference(rew,[status(thm),theory(equality)],[93,791]),
[iquote('7:Rew:93.0,791.0')] ).
cnf(806,plain,
equal(j(e23),e12),
inference(rew,[status(thm),theory(equality)],[805,53]),
[iquote('7:Rew:805.0,53.0')] ).
cnf(821,plain,
equal(op1(j(e21),j(e24)),e12),
inference(rew,[status(thm),theory(equality)],[806,181]),
[iquote('7:Rew:806.0,181.0')] ).
cnf(822,plain,
equal(op1(e12,e12),j(e21)),
inference(rew,[status(thm),theory(equality)],[806,172]),
[iquote('7:Rew:806.0,172.0')] ).
cnf(826,plain,
equal(j(e21),e11),
inference(rew,[status(thm),theory(equality)],[68,822]),
[iquote('7:Rew:68.0,822.0')] ).
cnf(875,plain,
equal(j(e24),e13),
inference(rew,[status(thm),theory(equality)],[63,799,806]),
[iquote('7:Rew:63.0,799.0,806.0,799.0')] ).
cnf(910,plain,
equal(e14,e12),
inference(rew,[status(thm),theory(equality)],[64,821,826,875]),
[iquote('7:Rew:64.0,821.0,826.0,821.0,875.0,821.0')] ).
cnf(911,plain,
$false,
inference(mrr,[status(thm)],[910,9]),
[iquote('7:MRR:910.0,9.0')] ).
cnf(912,plain,
~ equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[911,776]),
[iquote('7:Spt:911.0,775.0,776.0')] ).
cnf(913,plain,
( equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[775]),
[iquote('7:Spt:911.0,775.1,775.2')] ).
cnf(914,plain,
equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[913]),
[iquote('8:Spt:913.0')] ).
cnf(923,plain,
equal(op2(e21,e21),h(e12)),
inference(rew,[status(thm),theory(equality)],[914,209]),
[iquote('8:Rew:914.0,209.0')] ).
cnf(924,plain,
equal(op2(e21,h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[914,208]),
[iquote('8:Rew:914.0,208.0')] ).
cnf(944,plain,
equal(h(e12),e22),
inference(rew,[status(thm),theory(equality)],[87,923]),
[iquote('8:Rew:87.0,923.0')] ).
cnf(945,plain,
equal(j(e22),e12),
inference(rew,[status(thm),theory(equality)],[944,53]),
[iquote('8:Rew:944.0,53.0')] ).
cnf(958,plain,
equal(op1(e12,e12),j(e23)),
inference(rew,[status(thm),theory(equality)],[945,178]),
[iquote('8:Rew:945.0,178.0')] ).
cnf(961,plain,
equal(op1(j(e24),j(e23)),e12),
inference(rew,[status(thm),theory(equality)],[945,167]),
[iquote('8:Rew:945.0,167.0')] ).
cnf(965,plain,
equal(j(e23),e11),
inference(rew,[status(thm),theory(equality)],[68,958]),
[iquote('8:Rew:68.0,958.0')] ).
cnf(977,plain,
equal(h(e13),e24),
inference(rew,[status(thm),theory(equality)],[88,924,944]),
[iquote('8:Rew:88.0,924.0,944.0,924.0')] ).
cnf(978,plain,
equal(j(e24),e13),
inference(rew,[status(thm),theory(equality)],[977,54]),
[iquote('8:Rew:977.0,54.0')] ).
cnf(1031,plain,
equal(e12,e10),
inference(rew,[status(thm),theory(equality)],[72,961,978,965]),
[iquote('8:Rew:72.0,961.0,978.0,961.0,965.0,961.0')] ).
cnf(1032,plain,
$false,
inference(mrr,[status(thm)],[1031,2]),
[iquote('8:MRR:1031.0,2.0')] ).
cnf(1033,plain,
~ equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1032,914]),
[iquote('8:Spt:1032.0,913.0,914.0')] ).
cnf(1034,plain,
equal(h(e11),e20),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[913]),
[iquote('8:Spt:1032.0,913.1')] ).
cnf(1041,plain,
equal(op2(h(e13),e20),e20),
inference(rew,[status(thm),theory(equality)],[1034,554]),
[iquote('8:Rew:1034.0,554.0')] ).
cnf(1045,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[1041,555]),
[iquote('8:Rew:1041.0,555.0')] ).
cnf(1048,plain,
equal(op2(h(e12),e20),e20),
inference(rew,[status(thm),theory(equality)],[1045,556]),
[iquote('8:Rew:1045.0,556.0')] ).
cnf(1051,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[557,1048]),
[iquote('8:Rew:557.0,1048.0')] ).
cnf(1053,plain,
equal(op2(h(e14),e20),e20),
inference(rew,[status(thm),theory(equality)],[1051,552]),
[iquote('8:Rew:1051.0,552.0')] ).
cnf(1059,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[1053,553]),
[iquote('8:Rew:1053.0,553.0')] ).
cnf(1060,plain,
equal(j(e20),e14),
inference(rew,[status(thm),theory(equality)],[1059,55]),
[iquote('8:Rew:1059.0,55.0')] ).
cnf(1063,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[548,1060]),
[iquote('8:Rew:548.0,1060.0')] ).
cnf(1064,plain,
$false,
inference(mrr,[status(thm)],[1063,4]),
[iquote('8:MRR:1063.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG081+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 22:23:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 468 clauses, backtracked 458 clauses, performed 8 splits and kept 861 clauses.
% 0.19/0.49 SPASS allocated 85613 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.00 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.04 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 4, length 220 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : ax1 ax2 co1 ax4 ax5
% 0.19/0.50
%------------------------------------------------------------------------------